Put x = tanθ

⇒ θ = tan^–1(x)

tan^–1{tanθ +}

= tan^–1{tanθ +}

= tan^–1{tanθ +secθ }

= tan^–1

= tan^–1

Sinθ = ,cosθ =

= tan^–1

= tan^–1

= tan^–1

Dividing by we get,

= tan^–1

= tan^–1

= tan^–1

tan(x+y) =

= tan^–1

=

From 1 we get

= ^.

Therefore, the simplification of given equation is ^.